# Binary and Bases

Learn about binary and other bases.

StartBinary and Bases: Lesson

Lesson 1 of 1

- 1We use number bases every day without realizing it. When we think about numbers in everyday life, we are almost always thinking of decimal numbers, or numbers in base 10, where each digit of a numb…
- 2While we as humans intuitively use decimal base in our everyday lives, there are other base systems that are very important to mathematics and computers. For example, binary, base 2, is the underly…
- 3Now that we’ve discussed how a binary number is represented, as well as some important reasons we use binary numbers, we might wonder how computers can convert binary numbers to decimal numbers (th…
- 4Another method we can use to convert numbers from one base to another is using what is known as the division method. In the division method, we divide a decimal number by the value of the base as m…
- 5Any number can be a base; however, only a few are common on computers. The ones we discussed previously (hexadecimal, decimal, octal, and binary) are the most common on computer systems. Octal num…
- 6We can convert octal to decimal in the same way we converted binary to decimal. For example, we use the powers of eight just as we did in the lookup table to convert 0o456 to decimal: | power | …
- 7We convert decimal to octal in the same way we convert decimal to binary. We can use the division method with the base of 8 and reverse the numbers at the end. We start with the decimal number and …
- 8Hexadecimal (base 16), often called “hex,” is a convenient and concise way to represent binary numbers on a computer. Hex numbers are often used for values like colors and any other place where we …
- 9We can convert hexadecimal to decimal in a similar way we converted binary to decimal, using the powers method. As a reminder, hexadecimal digits have 16 possible values, 0-9 and
*a-f*. A famous h… - 10We use the same division technique for octal and binary to convert decimal to hexadecimal, except we divide using 16. We will use decimal 112 again. | Division by 16 | Remainder | Hex | | ——…

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